Finite Group Databasebeta

← #14571963

Subgroups — #14571963

Order 2432.

688 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597332C211yesmaximal, characteristic, complemented
2C2×#10597381C211yesmaximal, characteristic, complemented
3C2×#10597385C211yesmaximal, characteristic
4C22×C4×Dic19C211yesmaximal, characteristic, complemented
5#11926444C212yesmaximal, complemented
6#11926441C212yesmaximal, complemented
7#11926437C212yesmaximal, complemented
8#11926433C212yesmaximal, complemented
9#11926423C211yesmaximal, characteristic, complemented
10#11926402C211yesmaximal, characteristic, complemented
11C19×#386C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C23×C4×C19C2211yescharacteristic
14C22×C22⋊D19C2211yescharacteristic
15C22×C22⋊D19C2211yescharacteristic
16C23×Dic19C2211yescharacteristic
17C23×Dic19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2212yes—
20C2×C22⋊Dic19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2211yescharacteristic
23#10597385—24no—
24#10597381—24no—
25C2×(C2×D19)⋊C4C2212yes—
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×C4⋊Dic19C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2212yes—
31C2×Dic19⋊C4C2211yescharacteristic
32C2×C4×Dic19—24no—
33C2×C4×Dic19C2212yes—
34C2×C4×Dic19C2212yes—
35#10597332—24no—
36C19×#95C2212yes—
37C19⋊#95C2212yes—
38C19⋊#95C2212yes—
39C24×C19C2311yescharacteristic
40C24×C19C2311yescharacteristic
41C23×D19C2311yescharacteristic
42C2×D4×C19—22no—
43C2×D4×C19—22no—
44C2×D4×C19—22no—
45C22×C4×C19—22no—
46C22×C4×C19—24no—
47C22×C4×C19C2312yes—
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2312yes—
50C2×C22⋊D19—22no—
51C2×C22⋊D19—22no—
52C2×C22⋊D19—22no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—24no—
55C22×Dic19—22no—
56C22×Dic19—22no—
57C22×Dic19—24no—
58C22×Dic19D414yes—
59C22×Dic19D414yescomplemented
60C22×Dic19C2312yes—
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2312yes—
64C22×Dic19C2311yescharacteristic
65C22⋊C4×C19—22no—
66C22⋊C4×C19—24no—
67C22⋊Dic19—22no—
68C22⋊Dic19—24no—
69C22⋊Dic19—22no—
70(C2×D19)⋊C4—24no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4—24no—
73C4⋊Dic19—24no—
74Dic19⋊C4—24no—
75Dic19⋊C4—22no—
76Dic19⋊C4—24no—
77C4×Dic19—24no—
78C4×Dic19—24no—
79C23×C19—22no—
80C23×C19—22no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—21no—
86C23×C19C2×D412yes—
87C23×C19C2×D412yes—
88C23×C19#4112yes—
89C23×C19C2411yescharacteristic
90C22×D19—21no—
91C22×D19—21no—
92C22×D19—22no—
93C22×D19—21no—
94C22×D19—22no—
95D4×C19—44no—
96C2×C4×C19—28no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—21no—
105C2×C4×C19#4114yes—
106C22⋊D19—44no—
107C22⋊D19—44no—
108C2×Dic19—28no—
109C2×Dic19—22no—
110C2×Dic19—22no—
111C2×Dic19—22no—
112C2×Dic19—28no—
113C2×Dic19—22no—
114C2×Dic19—21no—
115C2×Dic19—21no—
116C2×Dic19—22no—
117C2×Dic19—22no—
118C2×Dic19—21no—
119C2×Dic19C2×D412yes—
120C2×Dic19C2×D414yes—
121C2×Dic19C2×D412yes—
122C2×Dic19#4114yes—
123#2854—191nomaximal, Sylow
124C22×C19—22no—
125C22×C19—22no—
126C22×C19—24no—
127C22×C19—24no—
128C22×C19—41no—
129C22×C19—41no—
130C22×C19—41no—
131C22×C19—42no—
132C22×C19—42no—
133C22×C19#12114yes—
134C22×C19C22×D411yescharacteristic
135C22×C19C22×D411yescharacteristic
136C22×C19C2×#4111yescharacteristic
137C22×C19C2×#4112yes—
138C22×C19C2×#4112yes—
139C2×D19—41no—
140C2×D19—41no—
141C2×D19—41no—
142C2×D19—42no—
143C2×D19—42no—
144C4×C19—24no—
145C4×C19—41no—
146C4×C19—42no—
147Dic19—24no—
148Dic19—22no—
149Dic19—41no—
150Dic19—42no—
151Dic19#12314yescomplemented
152C2×#123—191no—
153C2×#123—191no—
154C2×#121—191no—
155C22×C42—191no—
156#390—192no—
157#389—192no—
158#388—192no—
159#388—192no—
160#386—191no—
161#386D1911yescharacteristic, complemented
162#380—191no—
163C2×C19—24no—
164C2×C19—81no—
165C2×C19C2×#12111yescharacteristic
166C2×C19C2×#12311yescharacteristic
167C2×C19#52511yescharacteristic
168C2×C19#52912yes—
169C2×C19#53212yes—
170D19—81no—
171C22×D4—191no—
172C22×D4—191no—
173C22×D4C2×D1911yescharacteristic
174C23×C4—191no—
175C23×C4—191no—
176C23×C4C2×D1911yescharacteristic
177#123—384no—
178#123—384no—
179#121—384no—
180C2×C4⋊C4—191no—
181C2×C4⋊C4—192no—
182C2×C4⋊C4—192no—
183C2×C4⋊C4—192no—
184C2×C22⋊C4—191no—
185C2×C22⋊C4—191no—
186C2×C22⋊C4—192no—
187C2×C22⋊C4—191no—
188C2×C22⋊C4—192no—
189C2×C22⋊C4—192no—
190C2×C22⋊C4C2×D1911yescharacteristic
191C2×C22⋊C4C2×D1912yes—
192C2×C42—192no—
193C2×C42—192no—
194C2×C42—384no—
195#95—192no—
196#95—192no—
197#95C2×D1912yes—
198C19#285411yescharacteristic, complemented, Sylow
199C24—191no—
200C24C22×D1911yescharacteristic
201C24C22×D1911yescharacteristic
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—382no—
206C2×D4—384no—
207C2×D4—382no—
208C2×D4—382no—
209C2×D4—382no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—191no—
213C22×C4—194no—
214C22×C4—194no—
215C22×C4—191no—
216C22×C4—192no—
217C22×C4—192no—
218C22×C4—191no—
219C22×C4—384no—
220C22×C4—382no—
221C22×C4—382no—
222C22×C4C22×D1912yes—
223C22×C4C22×D1911yescharacteristic
224C22×C4C22×D1912yes—
225C4⋊C4—384no—
226C4⋊C4—382no—
227C4⋊C4—384no—
228C4⋊C4—384no—
229C22⋊C4—22no—
230C22⋊C4—24no—
231C22⋊C4—382no—
232C22⋊C4—384no—
233C22⋊C4—382no—
234C22⋊C4—384no—
235C22⋊C4—382no—
236C22⋊C4—384no—
237C42—384no—
238C42—384no—
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—22no—
245C23—22no—
246C23—381no—
247C23—381no—
248C23—381no—
249C23—382no—
250C23—382no—
251C23#6454112yes—
252C23D4×D1912yes—
253C23D4×D1912yes—
254C23C23×D1911yescharacteristic
255D4—44no—
256D4—764no—
257D4—764no—
258C2×C4—28no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—192no—
268C2×C4—194no—
269C2×C4—192no—
270C2×C4—194no—
271C2×C4—388no—
272C2×C4—382no—
273C2×C4—382no—
274C2×C4—382no—
275C2×C4—388no—
276C2×C4—381no—
277C2×C4—382no—
278C2×C4—381no—
279C2×C4—381no—
280C2×C4—382no—
281C2×C4—382no—
282C2×C4#6454314yes—
283C22—22no—
284C22—22no—
285C22—24no—
286C22—24no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—761no—
293C22—761no—
294C22—762no—
295C22—762no—
296C22—761no—
297C22#1059733014yes—
298C22C2×#6454111yescharacteristic
299C22C2×D4×D1911yescharacteristic
300C22C2×D4×D1911yescharacteristic
301C22C2×#6454312yes—
302C22#41×D1912yes—
303C4—24no—
304C4—42no—
305C4—41no—
306C4—194no—
307C4—382no—
308C4—384no—
309C4—762no—
310C4—761no—
311C2—24no—
312C2—81no—
313C2—1521no—
314C2C2×#1059733011yescharacteristic
315C2#123×D1911yescharacteristic
316C2#1192705011yescharacteristic
317C2#1192707412yes—
318C2#1192708912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#386C2
prime radicalC2×#10597385C2
hypercenter#386D19
hypocenterC19#2854
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10597332C2semidirect
2. C2×#10597381C2semidirect
4. C22×C4×Dic19C2semidirect
5. #11926444C2semidirect
6. #11926441C2semidirect
7. #11926437C2semidirect
8. #11926433C2semidirect
9. #11926423C2semidirect
10. #11926402C2semidirect
11. C19×#386C2semidirect
59. C22×Dic19D4semidirect
151. Dic19#123semidirect
161. #386D19semidirect
198. C19#2854semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#105973322
C2×#105973812
C2×#105973852
C22×C4×Dic192
#119264442
#119264412
#119264372
#119264332
#119264232
#119264022
C19×#3862
#285419